DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0022] A preferred embodiment of the present invention will be described below in detail with reference to the drawings.

[0023] An apparatus shown in FIG. 1 comprises a first camera 1, a second camera 2, a third camera 3, a control portion 4 and a calculating portion 5. The first camera 1, the second camera 2 and the third camera 3 are CCD cameras having a shutter function. The control portion 4 and the calculating portion 5 include a computer and a peripheral apparatus. The control portion 4 and the calculating portion 5 may be constituted by the same computer. A ball trajectory measuring apparatus may comprise a printing portion, a display portion and the like which are not shown.

[0024] The control portion 4 detects a trigger signal generated by hitting a golf ball and then transmits a signal to the calculating portion 5 in order to start to record image data. Moreover, the control portion 4 transmits a synchronizing signal toward the first camera 1, the second camera 2 and the third camera 3. A plurality of synchronized images is obtained by the first camera 1, the second camera 2 and the third camera 3 which receive the synchronizing signal.

[0025] The calculating portion 5 records, for each frame, image data obtained by the first camera 1, the second camera 2 and the third camera 3. For the recording, a time plus VTR, a digital disk recorder, an animation board or the like can be used. The data thus obtained are used for an image processing. In the image processing, a difference peak hold calculation is carried out in order of frames for the image data. More specifically, only a pixel memory for a changed peak in the pixel of each frame memory is held and other memories are erased. The image of a golf ball is whiter than a background and is obtained as the whitest portion in a decision of shading. Consequently, the background is erased by the image processing so that it is possible to obtain data in which only the image of the golf ball remains.

[0026] FIG. 2 is a typical side view showing a state in which the trajectory of the golf ball is measured by the apparatus in FIG. 1. FIG. 2 shows a golf ball G and a trajectory T of the golf ball G. The golf ball G flies from left to right in FIG. 2. In FIG. 2, Ps denotes a launch point and Pe denotes a drop point. As shown in FIG. 2, there can be supposed two-dimensional position coordinates in which the position of the first camera 1 is set to be an origin, a straight line connecting the first camera 1 and the second camera 2 is set to be an X axis and a direction of a height is set to be a Z axis.

[0027] The first camera 1 and the second camera 2 are provided behind the launch point Ps. The first camera 1 and the second camera 2 are placed in substantially the same position. The first camera 1 and the second camera 2 photograph the golf ball G from a back part. The third camera 3 is provided before the drop point Pe. The third camera 3 photographs the golf ball G from a front part. A distance between the first camera 1 and second camera 2 and the third camera 3 is represented as L. The position coordinates of the first camera 1 and the second camera 2 are (0, 0) and the position coordinates of the third camera 3 are (L, 0). The first camera 1, the second camera 2 and the third camera 3 are provided in such a manner that optical axes thereof are inclined upward in a horizontal direction. The inclination angle of the first camera 1 is greater than that of the second camera 2. The angle of view of the first camera 1 is surrounded by two-dotted chain lines L1a and L1b shown in FIG. 2. The angle of view of the second camera 2 is surrounded by two-dotted chain lines L2a and L2b. The angle of view of the first camera 1 partially overlaps with that of the second camera 2.

[0028] Description will be given to a method of calculating position coordinates (x, z) of the golf ball G by a triangulation method. When the golf ball G is launched, first of all, the golf ball G is photographed by the first camera 1 and the third camera 3. In this stage, the image of the golf ball G is not taken by the second camera 2. By the photographing, continuous image data are obtained. The image data obtained by the first camera 1 and the image data obtained by the third camera 3 make a pair. A black-and-white decision is carried out by horizontal scanning over frame data obtained by the first camera 1, and ball position in a vertical direction on the image are detected. Based on the result of the detection and a direction of an optical axis and an angle of view in the first camera 1, an angle of elevation θ₁ of the golf ball G in the position of the first camera 1 is calculated. Similarly, the black-and-white decision is carried out by the horizontal scanning over the frame data obtained by the third camera 3, and ball position in a vertical direction on the image are detected. Based on the result of the detection and a direction of an optical axis and an angle of view in the third camera 3, an angle of elevation θ₃ of the golf ball G in the position of the third camera 3 is calculated.

[0029] The following equation (1) is obtained by a triangle formed by a foot Pf of a perpendicular drawn from the golf ball G, and the first camera 1 and the golf ball G to be apexes.

tan θ₁=z/x (1)

[0030] On the other hand, the following equation (2) is obtained by a triangle formed by the foot Pf of the perpendicular drawn from the golf ball G, and the third camera 3 and the golf ball G to be apexes.

tan θ₃=z/(L−x) (2)

[0031] The following equations (3) and (4) are obtained from the equations (1) and (2).

x=(L·tan θ₃)/(tan θ₁+tan θ₃) (3)

z=(L·tan θ₁·tan θ₃)/(tan θ₁+tan θ₃) (4)

[0032] The distance L between the first camera 1 and the third camera 3 and the angles of elevation θ₁ and θ₃ which are calculated are substituted for the equations (3) and (4), and the position coordinates (x, z) of the golf ball G are calculated. The position coordinates (x, z) are obtained as time series data with the flight of the golf ball G.

[0033] As described above, the angle of view of the first camera 1 partially overlaps with that of the second camera 2. For a certain period of the flight, therefore, the image of the golf ball is photographed by both the first camera 1 and the second camera 2. The first camera 1 and the second camera 2 are synchronized with each other. Therefore, the angle of view of the first camera 1 and that of the second camera 2 are related to each other based on data on images photographed at the same time. In other words, the correspondence of the coordinates in the angle of view of the first camera 1 to those in the angle of view of the second camera 2 is grasped by calculating means.

[0034] When the golf ball G further flies, it gets out of the angle of view of the first camera 1. Then, the golf ball G is photographed by the second camera 2 and the third camera 3. Based on the image data obtained by the second camera 2 and the third camera 3, the position coordinates (x, z) of the golf ball G are calculated by the triangulation method. Since the angle of view of the first camera 1 is related to that of the second camera 2, continuous position coordinate data can be measured with high precision within a wide range of the trajectory T. As described above, the angles of view are related to each other based on the data on images photographed at the same time. Even if precision in the installation of the optical axis of the camera is insufficient, therefore, the position coordinates (x, z) are calculated with high precision.

[0035] In the method shown in FIG. 2, in the case in which the golf ball G flies without a substantial transverse shift from a target direction, measurement is carried out. If the flight is shifted from the target direction, a transverse direction (a perpendicular direction to the paper in FIG. 2) is set to be a Y axis. An angle of elevation of the golf ball G in the position of the first camera 1 is represented as θ₁₁, an angle of elevation of the golf ball G in the position of the third camera 3 is represented as θ₃₁, an angle in a transverse direction of the golf ball G in the position of the first camera 1 is represented as θ₁₂, and an angle in a transverse direction of the golf ball G in the position of the third camera 3 is represented as θ₃₂. θ₁₁, θ₃₁, θ₁₂ and θ₃₂ are obtained by an image processing based on the image data. Position coordinates (x, y, z) of the golf ball G are obtained by substituting θ₁₁, θ₃₁, θ₁₂ and θ₃₂ for the following equations (5), (6) and (7).

y=(L·tan θ₁₂·tan θ₃₂)/(tan θ₁₂+tan θ₃₂) (5)

0=((tan θ₁₁)²+(tan θ₃₁)²)·x²+2·(tan θ₃₁)²·L·x+((tan θ₁₁)²+(tan θ₃₁)²)·y²−(tan θ₃₁)²·L² (6)

0=(tan θ₁₁)²·(x²+y²)−z² (7)

[0036] Also in this case, the photographing is relayed by the first camera 1 and the second camera 2 which have mutual angles of view related to each other. Consequently, the measurement can be carried out within a wide range of the trajectory T.

[0037] At least three cameras for photographing the golf ball G from a back part may be provided to relay the photographing. At least two cameras for photographing the golf ball G from a front part may be provided to relay the photographing.

[0038] FIG. 3 is a typical side view showing another measuring method using the apparatus of FIG. 1. In this example, the first camera 1 is provided behind the launch point Ps, the second camera 2 is provided between the launch point Ps and the drop point Pe, and the third camera 3 is provided before the drop point Pe. The first camera 1 and the second camera 2 photograph the golf ball G from a back part. The third camera 3 photographs the golf ball G from a front part. The angle of view of the first camera 1 is surrounded by two-dotted chain lines L1a and L1b. The angle of view of the second camera 2 is surrounded by two-dotted chain lines L2a and L2b. The angle of view of the first camera 1 partially overlaps with that of the second camera 2. The angle of view of the first camera 1 is related to that of the second camera 2.

[0039] Also in the measuring method, first of all, the golf ball G is photographed by the first camera 1 and the third camera 3. The photographing of the first camera 1 is relayed to the second camera 2. Then, the golf ball G is photographed by the second camera 2 and the third camera 3. Based on image data thus obtained, the coordinate position (x, z) or (x, y, z) of the golf ball G is calculated by the triangulation method.

[0040] In an example shown in FIG. 3, the golf ball G is photographed immediately before a drop by the second camera 2. The Z coordinate of the golf ball G which is obtained immediately before the drop is small. If the second camera 2 is placed in the same position as the first camera 1, the angle of elevation of the golf ball G obtained immediately before the drop by the second camera 2 is small. On the other hand, if the second camera 2 is positioned between the launch point Ps and the drop point Pe as shown in FIG. 3, the angle of elevation of the golf ball G obtained immediately before the drop by the second camera 2 is comparatively great. The great angle of elevation contributes to an enhancement in precision in the measurement. The reason will be described below.

[0041] It is assumed that the position coordinates of the golf ball G obtained immediately before the drop are (200, 3), the position coordinates of the second camera 2 are (0, 0) and the position coordinates of the third camera 3 are (300, 0). In other words, it is assumed that the second camera 2 is provided behind the launch point Ps. In this case, an angle of elevation θ₂ of the golf ball G from the second camera 2 is calculated as 0.86 degree by the following equation.

θ₂=tan⁻¹ (3/200)

[0042] On the other hand, an angle of elevation θ₃ of the golf ball G from the third camera 3 is calculated as 1.72 degrees from the following equation.

θ₃=tan⁻¹ (3/(300−200))

[0043] If the angle of elevation θ₂ obtained based on the image data of the second camera 2 is 0.91 degree (that is, a value obtained with a shift of 0.05 degree from the original value of 0.86 degree), the position coordinates (x, y) of the golf ball G are calculated as (196.2, 3.1) by the following equation.

x=(300·tan(1.72))/(tan(0.91)+tan(1.72))

z=(300·tan(0.91)·tan(1.72))/(tan(0.91)+tan(1.72))

[0044] “196.2” to be the x coordinate thus calculated is smaller than “200” to be an actual x coordinate by 3.8.

[0045] In the case in which the position coordinates of the second camera 2 are (150, 0), in other words, the second camera 2 is close to the drop point Pe, the angle of elevation θ₂ is calculated as 3.43 degrees by the following equation.

θ₂=tan⁻¹(3/(200−150))

[0046] If the angle of elevation θ₂ obtained based on the image data of the second camera 2 is 3.48 degrees (that is, a value obtained with a shift of 0.05 degree from the original value of 3.43 degrees), the position coordinates (x, z) of the golf ball G are calculated as (199.6, 3.0) by the following equation.

x=(150·tan(1.72))/(tan(3.48)+tan(1.72))

z=(150·tan(3.48)·tan(1.72))/(tan(3.48)+tan(1.72))

[0047] “199.6” to be the x coordinate thus calculated is very close to “200” to be an actual x coordinate. Thus, the second camera 2 is provided in such a position that the golf ball G can be photographed immediately before the drop at a great angle of elevation. Consequently, the precision in the measurement can be enhanced.

[0048] In respect of the precision in the measurement, it is preferable that the second camera 2 should be provided in such a position that the inclination angle of the optical axis thereof is 3 to 40 degrees. The inclination angle is more preferably 5 to 40 degrees and particularly preferably 7 to 40 degrees. From the viewpoint of the precision in the measurement, it is preferable that the second camera 2 should be provided close to the third camera 3 from the middle point of the first camera 1 and the third camera 3.

[0049] It is preferable that the distances of the first camera 1, the second camera 2 and the third camera 3 from the ground should be 3 m or less. If the distance from the ground is more than 3 m, it is hard to measure the golf ball G immediately after the launch and immediately before the drop. From this viewpoint, it is more preferable that the distance from the ground should be 2 m or less. An ideal distance from the ground is zero.

[0050] At least three cameras for photographing the golf ball G from a back part may be provided to relay the photographing. At least two cameras for photographing the golf ball G from a front part may be provided to relay the photographing.

[0051] FIG. 4 is a typical side view showing a state in which the trajectory of a golf ball is measured by a ball trajectory measuring apparatus according to another embodiment of the present invention. This apparatus comprises a first camera 4, a second camera 5 and a third camera 6 which are the same as those of the apparatus in FIG. 1. This apparatus comprises the same components as the control portion 4 and the calculating portion 5 of the apparatus in FIG. 1, which are not shown.

[0052] The first camera 4 is provided before a drop point Pe, the second camera 5 is provided between a launch point Ps and the drop point Pe, and the third camera 6 is provided behind the launch point Ps. The first camera 4 and the second camera 5 photograph a golf ball G from the front part. The third camera 6 photographs the golf ball G from the back part. The angle of view of the first camera 4 is surrounded by two-dotted chain lines L1a and L1b. The angle of view of the second camera 5 is surrounded by two-dotted chain lines L2a and L2b. The angle of view of the first camera 4 partially overlaps with that of the second camera 5. The angle of view of the first camera 4 is related to that of the second camera 5.

[0053] In the measuring method, first of all, the golf ball G is photographed by the second camera 5 and the third camera 6. The photographing of the second camera 5 is relayed to the first camera 4. Then, the golf ball G is photographed by the first camera 4 and the third camera 6. Based on image data thus obtained, the coordinate position (x, z) or (x, y, z) of the golf ball G is calculated by the triangulation method.

[0054] In an example shown in FIG. 4, the golf ball G is photographed immediately after a launch by the second camera 5. The Z coordinate of the golf ball G which is obtained immediately after the launch is small. If the second camera 5 is placed in the same position as the first camera 4, the angle of elevation of the golf ball G obtained immediately after the launch by the second camera 5 is small. On the other hand, if the second camera 5 is positioned between the launch point Ps and the drop point Pe as shown in FIG. 4, the angle of elevation of the golf ball G obtained immediately after the launch by the second camera 5 is comparatively great. The great angle of elevation contributes to an enhancement in precision in the measurement.

[0055] In respect of the precision in the measurement, it is preferable that the second camera 5 should be provided in such a position that the inclination angle of the optical axis thereof in a horizontal direction is 3 to 40 degrees. The inclination angle is more preferably 5 to 40 degrees and particularly preferably 7 to 40 degrees. From the viewpoint of the precision in the measurement, it is preferable that the second camera 5 should be provided close to the third camera 6 from the middle point of the first camera 4 and the third camera 6.

[0056] At least two cameras for photographing the golf ball G from a back part may be provided to relay the photographing. At least three cameras for photographing the golf ball G from a front part may be provided to relay the photographing.

[0057] While the apparatus according to the present invention has been described above by taking, as an example, the case in which the trajectory of the golf ball G is measured, it is also suitable for measuring the trajectory of another ball.

[0058] The above description is only illustrative and can be variously changed without departing from the scope of the present invention.